The prolific Colombia striker, known as "the tiger" and coveted by several of Europe's richest clubs, took his tally for the season to 16 in 15 matches as Atletico restored their five-point lead over chasing city rivals Real Madrid.
The thumping victory at a festive Calderon also lifted them to within three points of unbeaten leaders Barcelona, who play at Real Betis in the late kickoff (2000 GMT).
Jose Mourinho's Real side twice had to come from behind to scrape a 3-2 win at Real Valladolid on Saturday which closed the gap to Atletico, whom they beat 2-0 at the Bernabeu last weekend, to two points overnight.
However, Atletico responded by romping to a 12th win in 15 outings this term against a Depor side in danger of dropping straight back down to the second division after winning promotion at the end of last season.
Atletico forward Diego Costa made amends for Thursday's Europa League red card when he opened the scoring with a header from Koke's corner in the 23rd minute.
Depor midfielder Juan Valeron headed against a post four minutes later but Atletico doubled their lead on their next foray forward when Falcao sped on to Koke's pass and fired a fizzing low drive into the corner of the net.
A quick throw on the left three minutes before the break set up the 26-year-old for his second and he crashed a dipping shot past Daniel Aranzubia from the corner of the penalty area.
Falcao then won and converted a penalty in the 64th minute to complete his hat-trick, flung himself to head Arda Turan's deflected shot over the line and netted a clinical fifth in the 71st minute.
He is the first player to score five goals in a La Liga match since Fernando Morientes for Real Madrid against Las Palmas in February 2002. (Reporting by Iain Rogers, editing by Ed Osmond)
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